7
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{65c47bd2-eace-4fec-b1e6-a0c904c4ec3f-4_474_912_260_493}
\captionsetup{labelformat=empty}
\caption{Fig. 1}
\end{figure}
A uniform solid cone of height 0.8 m and semi-vertical angle \(60 ^ { \circ }\) lies with its curved surface on a horizontal plane. The point \(P\) on the circumference of the base is in contact with the plane. \(V\) is the vertex of the cone and \(P Q\) is a diameter of its base. The weight of the cone is 550 N . A force of magnitude \(F \mathrm {~N}\) and line of action \(P Q\) is applied to the base of the cone (see Fig. 1). The cone topples about \(V\) without sliding.
- Calculate the least possible value of \(F\).
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{65c47bd2-eace-4fec-b1e6-a0c904c4ec3f-4_528_1143_1302_500}
\captionsetup{labelformat=empty}
\caption{Fig. 2}
\end{figure}
The force of magnitude \(F \mathrm {~N}\) is removed and an increasing force of magnitude \(T \mathrm {~N}\) acting upwards in the vertical plane of symmetry of the cone and perpendicular to \(P Q\) is applied to the cone at \(Q\) (see Fig. 2). The coefficient of friction between the cone and the horizontal plane is \(\mu\). - Given that the cone slides before it topples about \(P\), calculate the greatest possible value for \(\mu\).